問數,求最大值,求最大值,求最大值,求最大值

AM < or = QM
[sqrt(a) + sqrt(b) + sqrt(c)]/3 < or = sqrt{([sqrt(a)]^2 + [sqrt(b)]^2 + [sqrt(c)]^2)/3}
[sqrt(a) + sqrt(b) + sqrt(c)]/3 < or = sqrt[(a+b+c)/3] = sqrt(3/3) = 1
so sqrt(a) + sqrt(b) + sqrt(c) < or = 3
i.e. max value of sqrt(a) + sqrt(b) + sqrt(c) is 3

AM ≤ QM
(√a + √b + √c) / 3 ≤ √[(√a^2 + √b^2 + √c^2) / 3]
(√a + √b + √c) ≤ √[3 (a + b + c)]
(√a + √b + √c) ≤ √3